In fact, the networks which are most similar, once simple pairwise processes are discounted, are the Wikipedia Mathematician network Figure REF (b) and the Email network  Figure REF (d). In both cases, processes where an edge is added (upper triangle in the heat map) there is little difference from the pairwise model. This might be expected for the cases where there is at most one edge in the triplet. Only the \(\Delta \widehat{\mathsf {T}}_{23}\)  entry for the \(m_2 \rightarrow m_3\)  transition shows a slight increase over what would be predicted based on the rate of edge addition in these models (the \(p\)  parameter of the pairwise model) which suggests triadic closure [1]}, [2]}, [3]}, [4]} does play a role here but it is very slight by these measures. On the other hand, there is a strong sign of “triadic stability”, that is the complete graphlet \(m_3\)  is much more stable than we would expect given the rate of edge loss in the pairwise model (the \(q\)  parameter). It is natural to think that processes responsible for triadic closure (\(m_2 \rightarrow m_3\) ) would also slow the rate at which such triangles break up (\(m_3 \rightarrow m_2\) ) but we do not see this in our result. One interpretation of our results is that the social processes normally invoked for triadic closure [1]}, [2]}, [3]}, [4]} can, in some cases, be more important in preventing the breakup of triangles than in the creation of triangles.
